Reidemeister/Roseman-type Moves to Embedded Foams in 4-dimensional Space

J. Scott Carter

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arXiv · 1210.3608

Reidemeister/Roseman-type Moves to Embedded Foams in 4-dimensional Space

J. Scott Carter

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Abstract

The dual to a tetrahedron consists of a single vertex at which four edges and six faces are incident. Along each edge, three faces converge. A 2-foam is a compact topological space such that each point has a neighborhood homeomorphic to a neighborhood of that complex. Knotted foams in 4-dimensional space are to knotted surfaces, as knotted trivalent graphs are to classical knots. The diagram of a knotted foam consists of a generic projection into 4-space with crossing information indicated via a broken surface. In this paper, a finite set of moves to foams are presented that are analogous to the Reidemeister-type moves for knotted graphs. These moves include the Roseman moves for knotted surfaces. Given a pair of diagrams of isotopic knotted foams there is a finite sequence of moves taken from this set that, when applied to one diagram sequentially, produces the other diagram.

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BibTeX RIS

J. Scott Carter. 2012-10-12. Reidemeister/Roseman-type Moves to Embedded Foams in 4-dimensional Space. https://arxiv.org/abs/1210.3608

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